Cubic Spline Interpolation Approximations to Hadamard Integral Operator

Abstract

In this paper, we present cubic spline interpolation schemes for the Hadamard finite-part integral operator. The superconvergence of cubic spline rules for Hadamard finite-part integral is presented, and we prove the correctness of the reasoning in theory. Two examples are presented to confirm our theoretical analysis of approximations the Hadamard finite-part integrals and to show the accuracy of schemes for solving integral equations with a hypersingular kernel.